{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Discrete Distribution Functions\n",
    "\n",
    "- Binomial distribution\n",
    "- Poisson distribution (PMF, CDF, and PPF)\n",
    "\n",
    "Author:  Thomas Haslwanter, Feb-2017"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "# Note: here I use the modular approach, which is more appropriate for scripts\n",
    "# \"%pylab inline\" also loads numpy as np, and matplotlib.pyplot as plt\n",
    "%pylab inline\n",
    "import scipy.stats as stats"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Binomial Distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x2011c861ac8>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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cOgnpy+TJ0Lhx2bLERHjsMefntlhqOVaRWIKSnW08b/2fr05RzuAeTdffceOM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\n4kZiZmaluJGYmVkpfwN+Hr4krbYJAQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2011cb98438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "bd1 = stats.binom(20, 0.5)\n",
    "bd2 = stats.binom(20, 0.7)\n",
    "bd3 = stats.binom(40, 0.5)\n",
    "k = arange(40)\n",
    "plot(k, bd1.pmf(k), 'o-b')\n",
    "plot(k, bd2.pmf(k), 'd-r')\n",
    "plot(k, bd3.pmf(k), 's-g')\n",
    "title('Binomial distribition')\n",
    "legend(['p=0.5 and n=20', 'p=0.7 and n=20', 'p=0.5 and n=40'])\n",
    "xlabel('X')\n",
    "ylabel('P(X)')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Poisson Distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x2011dcb3908>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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KsoieJdCYUGHJIsxsq2mK6vYK8CaM6eNG4ak/wZL5eZYojBkGlizCyIn2LvY2\nnIi6O7f9lXoaqDrmnQTp6XUHInrSJ2NChSWLMFJR24xqdN653au3jeJHH5tNbIxw7bQxET9LoDGh\nwJJFGOlt3I6WOSz60jtL4HVFY5k7MZ3K+taInyXQmFAQPeNbR4Bth5rJShnBmFHR2bgNvGc2wIXT\nsvne6l0UjkmxdgtjgsyuLMLItpomZk5Ipe9ZbKPP1dO8E16t2RVdsyQa4wZLFmGirbObPUdao7q9\nwl9RTirZo0bwxm5LFsYEmyWLMLHzcAvdPRr1PaF8iQgLL8jm77vr6erucTscYyKaJYsw8e6d23Zl\n4evqadk0t3Wx1YYsNyaoLFmEie2HmkhLiic3PcntUELKlYXZxAi8Ye0WxgSVJYswsa2mmYsmpFnj\ntp+05HjmTExnjbVbGBNUlizCQEdXD7sOtzDD2iv6dPW0bN6paaK+pd3tUIyJWJYswsDuuhY6unus\nJ1Q/rp42BoA37erCmKCxZBEGtjtzbkfrHBaBFOWkkpViXWiNCSZLFmFgW00zKSPimJSR7HYoISkm\nxulCu6feZs8zJkgsWYSBbYeaKBqfSkyMNW73Z+G0bI6f7LQutMYESVCThYgsEpFdIlIpIg/0sX2E\niDznbF8vIvl+2yeKSKuI3B/MOENZV3cPFbXN1l4RwFVTs4gRWLPriNuhGBORgpYsRCQWeAy4HigC\nbheRIr9i9wCNqloI/Aj4jt/2HwJ/DlaM4WBvwwnaOnvszu0ARicnMDtvtLVbGBMkwbyymA9Uqupe\nVe0AVgI3+5W5GXjaef4C8D5xbiQQkQ8D+4DtQYwx5J0eltwatwO6etoYyqubaGi1LrTGDLVgJosJ\nwEGf5WpnXZ9lVLULaAIyRSQF+Crw8NleQETuFZFNIrKpvj6yvlEuX+Oh1NPAOzVNJMbHMCU7hVJP\nA8vXeNwOLWT1jkL79z2R9bdgTCgI1QbubwA/UtXWsxVS1cdVdZ6qzsvOzh6eyIbJrNw0lq4oY13l\nUYpyUlm/7yhLV5QxK4onPgpk5vg0slISbOgPY4IgmMmiBsjzWc511vVZRkTigDTgKHAp8F0R2Q/8\nG/A1EVkaxFhDTklBFv+7uJiddS10dStLV5SxbEmxTfJzFjExwlVTs3lzt3WhNWaoBTNZbASmishk\nEUkAFgMv+ZV5CbjTeX4r8Df1ulJV81U1H/gx8KiqLgtirCEpfWQCAOU1TXz80omWKAZg4bRsGk92\nUl5tXWicdKcuAAAVKElEQVSNGUpBSxZOG8RSYDVQATyvqttF5BERuckp9ku8bRSVwBeBM7rXRrMV\n6w8AcPeCfJ5dX0Wpp8HliELflVOzERuF1pghF9Q5uFV1FbDKb91DPs/bgNsCHOMbQQkuxJV6Gnhu\n00FyUhP5rxtncF3RWKuKGoDnNx1kStZI3thdz79fdwHgPZfl1U3vmb/bGHNuQrWBO+qVVR0nVoRr\nL/QOkldSkMWyJcWUVze5HFlom5WbxqHjbbx98DjHTnRQ6mmwjgHGDAFLFiHqsikZtHX1sKDw3auI\nkoIs+3YcQElBFl+7YToAD/yu3K7GjBkilixC1NrKo4jA5VMy3Q4l7Nxx6SRGJsTyyo466xhgzBCx\nZBGi1lY2UJSTerpHlBm4t/YdpVu9XWd/te6AdQwwZghYsghBpzq6Kas6/p4qKDMwvW0U3/zwTACu\nv2gcS1eUWcIw5jxZsghBG/cfo6O7h5ICq4I6V+XVTSxbUswtc/OYOymdDfuOsex26xhgzPmyZBGC\n1noaiI8V5k/OcDuUsHPfwoLTbRS3zc3FU3+CxIRY6xhgzHmyZBGC1nmOUpyXTnJCUG+DiXgfnJVD\nYnwMv91U7XYoxoQ9SxYhpulkJ+/UNHG5VUGdt1GJ8dxwUQ5/evsQpzq63Q7HmLBmySLErNt7FFWs\ncXuI3DY3j5b2LlZvP+x2KMaENUsWIabU00BSfCyz80a7HUpEuHRyBnkZSfx288HAhY0x/bJkEWLW\nVjYwf3IGCXH2qxkKMTHCrXPyWFt5lIPHTrodjjFhyz6RQsjhpjY89SdYUGjtFUPplrkTEIHfbbGG\nbmMGy5JFCFm313vjmA1PMbRy05MpKcjkhc3V9NikSMYMiiWLELK28iijk+Mpykl1O5SIc9vcPKob\nT/HWvqNuh2JMWLJkESJUldLKBi6fkklMjLgdTsT5wIxxjBoRxwt2z4Uxg2LJIkTsP3qSQ01tlFiX\n2aBISojlxtnjWbWtlpa2TrfDMSbsWLIIEWsrve0VC+xmvKC5bW4ubZ09vFxe63YoxoQdSxYhotTT\nQE5aIpOzRrodSsSanTeawjEp/HazVUUZc64sWYSAnh5lnecoJQVZiFh7RbCICLfNzWXzgUY89a1u\nh2NMWLFkEQIqDjfTeLLT7q8YBi3tXcQI7xlcsNTTwPI1HhejMib0WbIIAaWV3u6cNh5U8JUUZBIb\nI6zcUEVXd8/pyZJm5aa5HZoxIS2oyUJEFonILhGpFJEH+tg+QkSec7avF5F8Z/11IrJZRN5xfl4b\nzDjdttbTQEH2SMamJrodSsQrKchi6TVTOX6qk8//poylK8pYtqTYboQ0JoCgJQsRiQUeA64HioDb\nRaTIr9g9QKOqFgI/Ar7jrG8AblTVi4A7gWeCFafbOrp62LDvmH1YDaPPXVNARnI8f952mNsvybNz\nb8wABPPKYj5Qqap7VbUDWAnc7FfmZuBp5/kLwPtERFS1TFUPOeu3A0kiMiKIsQ675Ws8lHoaKK8+\nzsmObhYUZlrd+TDZsP8YHd3eYT+eLN1v83MbMwDBTBYTAN9xoauddX2WUdUuoAnwb+W9Bdiiqu3+\nLyAi94rIJhHZVF9fP2SBD4dZuWksXVHGyg0HEYFYEas7Hwa9bRSPf2IuJQWZxAh87tdbLGEYE0BI\nN3CLyAy8VVP/0td2VX1cVeep6rzs7OzhDe48lRRksWxJMX/YWkN2ygi++uI7Vnc+DMqrm7znuTCL\nr91wIa3t3VxRmE15dZPboRkT0oKZLGqAPJ/lXGddn2VEJA5IA446y7nA74FPqmpE1s2MS02kq0c5\n0tLOxy+daIliGNy3sOD0eZ45IY2PFk9g9Y7D3HjxeJcjMya0BTNZbASmishkEUkAFgMv+ZV5CW8D\nNsCtwN9UVUVkNPAy8ICqrg1ijK769p93AnDPFfk8u77KqkJc8KUPTAPg+6t3uRyJMaEtaMnCaYNY\nCqwGKoDnVXW7iDwiIjc5xX4JZIpIJfBFoLd77VKgEHhIRLY6jzHBitUNr+6o45UddVw5NYv//NAM\nli0pZumKMksYw2zC6CTuuWIyvy+rYVuNVUUZ0x9RjYzJYObNm6ebNm1yO4wB+9RTG/nbziP86fNX\nMHOCt1Hb2zuqifsWFrgcXXRpbuvk6u+9wbSxo1jx6UttyBUTVURks6rOC1QupBu4I1V3j7K7roX5\n+RmnEwV4G70tUQy/1MR4/vV9U1m39yiv7zridjjGhCRLFi54dUcd1Y2nuHtBvtuhGMeSSycyOWsk\nj67aSVd3j9vhGBNyLFm44Mm1+5gwOonrisa6HYpxxMfG8NVF06k80srzNpueMWewZDHMth9qYv2+\nY9xZMom4WDv9oWRfQysXjE3hh6/uprW9C7ARaY3pZZ9Ww+zJtftJTojlY/Mmuh2K8XNx3mgON7XR\n0NrO42/utRFpjfFhyWIY1be089LWQ9wyJ5e05Hi3wzF+SgqyWP6JuSTExvDY63v4zLOb7a56YxyW\nLIbRivVVdHT3cJc1bIeskoIsPn7ZRLp7vL3WpmSluB2SMSHBksUwae/q5tn1B7h6WjYF2fYBFKpK\nPQ38YeshFs/Po7W9m4/9bN3p9gtjopkli2Hycnkt9S3t3L1gstuhmH70tlEsW1LMtz86i68umsaB\nYydZ8vO3rDutiXqWLIaBqvLE2n0UjknhqqlW/x2qTo9I67RRfObqQv75ysmUVzfxn3/cTqSMdmDM\nYMS5HUA02HSgkW01zfzPh2faUBIhrK+75//jg0UkxMbwkzc85GUk8dmrC12IzBj32ZVFkPTOhAfe\nm/DSkuKZMDrR+uyHofvfP42bLh7Pd/+yiz9u9R9l35joYMkiSHpnwntpaw1/2XaYK6dm8aXflluf\n/TAUEyN877ZZ5KUn8aXn32b93qOnt9lNeyZaWLIIkt6Z8L78Qjmq8I89DdZnP4yNiIvloQ8V0aPK\np57aiKe+1W7aM1HF2iyCaFtNE+1d3l40n7x8kiWKMHfdjHH86J9m82/PbeXG//0HsTHCzz4x136v\nJirYlUWQPLexikdX7SQhNoal1xTaTHgR4ubiCdx+aR4nO7ppaevi5fJaTth9GCYKWLIIglXv1PLA\n794hPlb4xZ3zuP8D02wmvAhR6mngL9vq+OzVBSTGx/Dr9VUs+j9vvqcdw5hIZMliiL25u55/XVnG\n+NFJ/PwT87jqgmzg3TaM8mqbujNc+d6095VF03nirksYlRhHR1cPi3/+FrctL+UNv8mTrAHcRAqb\nVnUIbT5wjI//YgOTs0bym3svIy3JBguMJMvXeJiVm/aeNopSTwOb9zdypKWdZ946QIzAwzfN4BOX\n578nuVi7hglVA51W1ZLFIPl/cFTUNnPLT9YyIj6WV/59IdmjRgxbLCY0/H2P96ry2IlOZk5Ipero\nSZZ/fC4lhZYoTOiyObiDrPc+ilJPA/sbTvCxn71FW1cPD980wxJFlLpyajav338NM8ansq2mmea2\nLh750w5+8fe9NLS2v+dGzV5WTWXChSWLQeptg7jvmc3cuOwftLR18t1bZnHT7Aluh2ZctP1QE7VN\nbdx75RSSE2Lp7O7hf16u4LJ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      "text/plain": [
       "<matplotlib.figure.Figure at 0x2011dc44588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pd = stats.poisson(10)\n",
    "plot(k, pd.pmf(k),'x-')\n",
    "title('Poisson distribition - PMF')\n",
    "xlabel('X')\n",
    "ylabel('P(X)')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Different Views of the Poisson Distrubution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x2011dd74ef0>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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5NOpyRKSNCLP7CHefA8ypN+6uhNcXhPnzpXG/f309m0rLeOqm03XROxGpo7VB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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2011dd91f98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "k = arange(30)\n",
    "plot(k, pd.cdf(k))\n",
    "title('Poisson distribition - CDF')\n",
    "xlabel('X')\n",
    "ylabel('P(X)')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x2011dd799e8>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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lzU47pnyTlM8wzMxKqXrCkFQHfB24HJgPXClpfo9iHwRaIuJk4CvAP6QZ04H2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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2011de275c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "y = linspace(0,1,100)\n",
    "plot(y, pd.ppf(y))\n",
    "title('Poisson distribition - PPF')\n",
    "xlabel('X')\n",
    "ylabel('P(X)')"
   ]
  }
 ],
 "metadata": {
  "celltoolbar": "Slideshow",
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
